Updated: Rep. Pete Sessions now supports his NRCC deputy, Rep. Greg Walden, R-Ore., to take over next year. Sessions’ spokeswoman Torrie Miller emails: “Congressman Sessions fully supports Congressman Greg Walden to take on the NRCC Chairmanship in 2013. That said, both Sessions and Walden are solely focused on their current jobs to strengthen the Republican Majority on November 6th.”

As recently as yesterday, Sessions seemed to be entertaining the idea of seeking another term as NRCC chairman.

Sessions serves as vice-chairman of the powerful panel, which controls how bills are debated and amended, and whose chairman typically takes a high profile role in floor debates.

The current chairman is retiring. But Politico reports that many GOP lawmakers see Rep. Doc Hastings, R-Wash., as a stronger contender and better choice to replace him. Sessions has begun talking about seeking a third two-year term as head of the party’s House campaign arm — fueling speculation that he knows he’s unlikely to get the Rules gavel, Politico reports.

Speaker John Boehner gets to handpick the senior Republican on Rules. Hastings currently chairs the Natural Resources Committee.

“I don’t think it’s a given that I want to leave the [NRCC] yet,” Sessions told Politico. “I’m having so much fun doing this, I may want to run as chairman again.”

He succeeded Oklahoma Rep. Tom Cole as head of the National Republican Congressional Committee in late 2009, and presided over the party’s historic gains in the 2010 elections. He told Politico that he’ll decide whether to seek another term after the Nov. 6 elections.

A Sessions spokeswoman said today that his comments about seeking a third NRCC term were made “in jest.”

Politico noted that Sessions’ deputy, Rep. Greg Walden of Oregon, “has been openly telling colleagues he plans to run for NRCC chairman.”